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Blow-up of solutions for a viscoelastic equation with nonlinear damping

100%
Zhifeng Y.
Open Mathematics
|
2008
|
tom 6
|
nr 4
568-575
EN
The initial boundary value problem for a viscoelastic equation with nonlinear damping in a bounded domain is considered. By modifying the method, which is put forward by Li, Tasi and Vitillaro, we sententiously proved that, under certain conditions, any solution blows up in finite time. The estimates of the life-span of solutions are also given. We generalize some earlier results concerning this equation.
2
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An arc-analytic function with nondiscrete singular set

100%
Kurdyka K.
Annales Polonici Mathematici
|
1994
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tom 59
|
nr 3
251-254
EN
We construct an arc-analytic function (i.e. analytic on every real-analytic arc) in ℝ² which is analytic outside a nondiscrete subset of ℝ².
3
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Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions

88%
Nouioua F., Basti B.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2021
|
tom 20
43-56
EN
This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder's and Banach's fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.
4
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Full discretization of some reaction diffusion equation with blow up

75%
Barro G., Mampassi B., Some L., Ntaganda J., So O.
Open Mathematics
|
2006
|
tom 4
|
nr 2
260-269
EN
This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow - up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.
5
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Existence and nonexistence results for reaction-diffusion equations in product of cones

63%
Hamidi A., Laptev G.
Open Mathematics
|
2003
|
tom 1
|
nr 1
61-78
EN
Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.
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